A154128 a(n) = 5^n*(n+4)!/n!.

24, 600, 9000, 105000, 1050000, 9450000, 78750000, 618750000, 4640625000, 33515625000, 234609375000, 1599609375000, 10664062500000, 69726562500000, 448242187500000, 2838867187500000, 17742919921875000, 109588623046875000

Offset: 0

Author

Omar E. Pol, Jan 05 2009

Keywords

• easy
• nonn

Comments

Column 4 of square array A152818.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (25, -250, 1250, -3125, 3125).

Crossrefs

Cf. A000142, A006043, A006044, A152818, A154120.

Programs

Magma

[5^n*(n+4)*(n+3)*(n+2)*(n+1): n in [0..20]]; // Vincenzo Librandi, Aug 15 2011

Mathematica

LinearRecurrence[{25, -250, 1250, -3125, 3125}, {24, 600, 9000, 105000, 1050000}, 25] (* or *) Table[5^n*(n+4)*(n+3)*(n+2)*(n+1), {n,0,25}] (* G. C. Greubel, Sep 02 2016 *)

Formula

a(n) = 5^n*(n+4)*(n+3)*(n+2)*(n+1).

From R. J. Mathar, Feb 06 2009: (Start)

a(n) = A052762(n+4)*A000351(n).

a(n) = 24*A036071(n).

G.f: 24/(1-5*x)^5. (End)

From G. C. Greubel, Sep 02 2016: (Start)

a(n) = 25*a(n-1) - 250*a(n-2) + 1250*a(n-3) - 3125*a(n-4) + 3125*a(n-5).

E.g.f.: (24 + 480*x + 1800*x^2 + 2000*x^3 + 625*x^4)*exp(5*x). (End)

Extensions

More terms from R. J. Mathar, Feb 06 2009